We present a study of the average X-ray spectral properties of the sources detected by the NuSTAR extragalactic survey, comprising observations of the E-CDFS, EGS and COSMOS fields. The sample includes 182 NuSTAR sources (64 detected at 8-24 keV), with 3-24 keV fluxes ranging between $f_{rm 3-24 keV}approx10^{-14}$ and $6times10^{-13}$ erg/cm$^2$/s ($f_{rm 8-24 keV}approx3times10^{-14}-3times10^{-13}$ erg/cm$^2$/s) and redshifts of $z=0.04-3.21$. We produce composite spectra from the Chandra+NuSTAR data ($Eapprox2-40$ keV, rest frame) for all the sources with redshift identifications (95%) and investigate the intrinsic, average spectra of the sources, divided into broad-line (BL) and narrow-line (NL) AGN, and also in different bins of X-ray column density and luminosity. The average power-law photon index for the whole sample is $Gamma=1.65_{-0.03}^{+0.03}$, flatter than $Gammaapprox1.8$ typically found for AGN. While the spectral slope of BL and X-ray unabsorbed AGN is consistent with typical values ($Gamma=1.79_{-0.01}^{+0.01}$), a significant flattening is seen in NL AGN and heavily-absorbed sources ($Gamma=1.60_{-0.05}^{+0.08}$ and $Gamma=1.38_{-0.12}^{+0.12}$, respectively), likely due to the effect of absorption and to the contribution from Compton reflection to the high-energy flux (E>10 keV). We find that the typical reflection fraction in our spectra is $Rapprox0.5$ (for $Gamma=1.8$), with a tentative indication of an increase of the reflection strength with column density. While there is no significant evidence for a dependence of the photon index with X-ray luminosity in our sample, we find that $R$ decreases with luminosity, with relatively high levels of reflection ($Rapprox1.2$) for $L_{rm 10-40 keV}<10^{44}$ erg/s and $Rapprox0.3$ for $L_{rm 10-40 keV}>10^{44}$ erg/s AGN, assuming $Gamma=1.8$.
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